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There are two alloys, A and B, of copper and zinc. The ratio (by

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Manager
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There are two alloys, A and B, of copper and zinc. The ratio (by  [#permalink]

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New post 25 Nov 2019, 03:50
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There are two alloys, A and B, of copper and zinc. The ratio (by weight) of copper and zinc in alloy A is 8 : 1 and that in alloy B is 2 : 7. It is found that, if alloy A and alloy B are mixed in a certain ratio, the weights of copper and zinc in the resultant alloy are also in that ratio. What is that ratio?

(A) 4 : 3
(B) 3 : 2
(C) 5 : 3
(D) 2 : 1
(E) 3 : 1
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Re: There are two alloys, A and B, of copper and zinc. The ratio (by  [#permalink]

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New post 26 Nov 2019, 06:52
Alloy A = c : z = 8 : 1
Alloy B = c : z = 2 : 7

I tested the answer values for this problem.

Answer B gives ratio A : B = 3 : 2, which means that copper and zinc ratio of A becomes 24 : 3 (8×3 and 1×3) and B becomes 2 : 14.
Which means that the weight ratio of A : B equals 24+3 = 27 to 2+14 = 16 which does not equal to 3:2

Answer D gives ratio A : B = 2 : 1. With the same logic as above this results in A 16 : 2 and B 2:7.
This give a total weight ratio of 18 : 9 which equals 2:1

There should be an easier method but this is how I have done it.
ANS D
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There are two alloys, A and B, of copper and zinc. The ratio (by  [#permalink]

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New post 26 Nov 2019, 11:41
weight of copper is 8gm in 9gm of alloy A and 2gm in 9 gm of alloy B

8..................2
....... x.......
x...............9-x

\(\frac{8-x}{x-2}=\frac{9-x}{x}\)

3x=18

x=6

Ratio= 6 : (9-6)= 2:1




CaptainLevi wrote:
There are two alloys, A and B, of copper and zinc. The ratio (by weight) of copper and zinc in alloy A is 8 : 1 and that in alloy B is 2 : 7. It is found that, if alloy A and alloy B are mixed in a certain ratio, the weights of copper and zinc in the resultant alloy are also in that ratio. What is that ratio?

(A) 4 : 3
(B) 3 : 2
(C) 5 : 3
(D) 2 : 1
(E) 3 : 1
Manager
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S
Joined: 09 Nov 2015
Posts: 154
There are two alloys, A and B, of copper and zinc. The ratio (by  [#permalink]

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New post 28 Nov 2019, 01:36
Let the required ratio be: Cu:Zn=x:y and the resultant alloy be called Alloy C. This means that 8x units of Cu and '1x' units of Zn from Alloy A will be combined with 2y units of Cu and 7y units of Zn from Alloy B to produce Alloy C which will then contain (8x+2y) units of Cu and (x+7y) units of Zn.
Therefore, in Alloy C, Cu:Zn=(8x+2y):(x+7y) which is equal to the ratio in which A and B were combined, i.e x/y.
Therefore, (8x+2y)/(x+7y)=x/y....> 2y^2+xy-x^2=0....> 2y^2+2xy-xy-x^2=0...> 2y(y+x)-x(y+x)=0....> (2y-x)(y+x)=0....> 2y-x=0...> x/y=2/1
ANS: D
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There are two alloys, A and B, of copper and zinc. The ratio (by   [#permalink] 28 Nov 2019, 01:36
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